Question

A parallel beam of monochromatic light falls normally on a single slit of width \( a \) and a diffraction pattern is observed on a screen placed at a distance \( D \) from the slit. Explain:
the formation of maxima and minima in the diffraction pattern, and
why the maxima go on becoming weaker and weaker with increasing order \( (n) \).

Hint:

Single-slit diffraction:

Minima: \( a\sin\theta = n\lambda \)
Central maximum brightest and widest
Intensity falls off for higher orders

Answer 1

Diffraction of Light through a Single Slit
Consider a parallel beam of monochromatic light falling normally on a single slit of width a. A diffraction pattern is observed on a screen at a distance D from the slit. Let the wavelength of light be λ.

Step 1: Formation of Maxima and Minima
The diffraction occurs due to the interference of light waves originating from different points across the slit width. According to the principle of superposition:
- For minima (dark fringes), light from different parts of the slit interferes destructively. The condition for minima is:
a sin θ = n λ, where n = 1, 2, 3,...
Here θ is the angle between the central axis and the direction of the dark fringe.
- For maxima (bright fringes), light interferes constructively. These occur approximately halfway between minima. However, their exact positions require more detailed calculations and are not exactly at regular intervals like minima.
The central maximum is the brightest, and the first-order maxima are less bright than the central maximum.

Step 2: Why Maxima Weaken with Increasing Order
- As the order n increases, the path difference between waves from different parts of the slit becomes larger. - More destructive interference occurs within each region contributing to a maximum. - As a result, the intensity of higher-order maxima decreases, making them weaker and less bright.
Step 3: Summary
- Minima (dark fringes) occur at a sin θ = n λ, n = 1, 2, 3,...
- Maxima occur approximately between minima and get weaker with increasing order due to increasing destructive interference.
- The central maximum is the brightest, and intensity falls off for higher-order maxima.